Tor Olav Kristensen wrote:
> 
> Dan,
> 
> are you sure that your new basis vectors are
> orthogonal to each other ?

They aren't that's the primary problem
 
> I.e.: You should get three zeros every time.
> (Let me know if you think that I'm wrong about this.)

You are right.  The idea was to create a skewed matrix, and then fix it
so that it is a rotation matrix, instead of a rotation, plus a bunch of
sheers and scales.  
 
> Tor Olav
> 
> P.S.:
> It's possible to do some simplifications to you macros  ;)
> 
> - And I think that you don't even have to use quats.
> When you have got yourself some orthogonal basis vectors,
> then just normalize them in order to make them orthonormal.
> And then try to use them directly within the matrix.

I know I don't have to use quats, but I don't know how to normalize a
matrix (remove the skew).  All of the quaternion functions I used were
already in my library.  It was a convenient way to get an idea of what
things would look like with a matrix algebra solution.  The formula I
used for converting a matrix to a quaternion is only designed to work
with normalized rotation matrices, so I was pleased that my bad math
worked relatively close to what I was looking for.  
-- 
Dan Johnson 

http://www.geocities.com/zapob

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